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Unformatted text preview: DISCUSSION SECTION Tuesday 11/5: EXAM 2 – During your Monday 11/4: OPTIONAL review 8.61, 8.67–69 Thursday : Exercises 8.29, 8.33, 8.34, 8.38–41, 8.59, Wednesday : P. 334 – 338, 347–351, For Tomorrow : Exercises 8.18, 8.21–23, 8.25, 8.27 Today : P. 328 – 332 Assignments to within “B” units with conﬁdence. otherwise use . (p. 309) , . (p. 322) 225 HYPOTHESIS, – (p. 322) , light bulb ex. The “other” hypothesis is called the NULL manner What we are “trying to prove” in an objective, fair light bulb ex. ALTERNATIVE or RESEARCH hypothesis, – The hypothesis of MAIN INTEREST is the Parts of a statistical test. (p. 322) . if you have one, and solve for Use “ballpark” value for ©
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§ ! Type I error Reject Ho Type I error Type II error (p. 325) when true In our lightbulb example, saying when ’s that we pick. The test that we will discuss have the SMALLEST for the 226 saying what we “want” to say when we should not accepting and/or Correct Type II error Ha true (p. 323), SIGNIFICANCE Correct Accept Ho ¥ Reality
Ho true LEVEL of the test. ¥ ! ¥ ! ! ¡ £
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. forms the basis for our decision. gives values of TS for which 4. Rejection Region : (RR) depends on the choice of Compute value of TS Get data Do experiment Then 227 Make decision is REJECTED computed from the sample data using a formula 3. Test Statistic : (TS) 2. Alternative Hypothesis : 1. Null Hypothesis : Parts of a Statistical Test (p. 326) STA 2023 c D.Wackerly  Lecture 17 !
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¡ 3% ! 3% and because we usually do . . 228 , what kind of error could we judgement Don’t want to accept usually that is really true , so we reserve depends on the value of the parameter in – What is the probability of a TYPE II error? make? – If we accept do so. not know the probability of making an error if we – We do not ACCEPT REGION, we DO NOT REJECT If the value of the TS is NOT in the REJECTION REGION, we 3% ! If the value of the TS is in the REJECTION 3% ! Decision : STA 2023 c D.Wackerly  Lecture 17 Guilty : Innocent : Prosecutor : Experimenter Courtroom Analogy STA 2023 c D.Wackerly  Lecture 17 !
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&% 3% ! ¥ 229 Test Statistic, TS Rejection Region, RR ! Need In this case, Lightbulb Example : a ﬁxed particular value of about a Population Mean, Large Sample Hypothesis Testing &% 34%
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α type I error Want ! ! ! ¦ “something” in favor of than . by a “lot” of standard errors. is probably than The true value of is is POSITIVE and LARGE true value is. © ! ! ! ¢ ) &% ( ) 0 ) ) © 0 § 3) 3
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true mean lifelength of ALL BULBS Ex. : Lightbulb Example “Upper Tail test”, “One Tail Test” (p. 329) ! Data : !
! © , whatever that § ) ¢ ) ¨2 ¡ level test, RR : is close to the true value of ¢ FACT: £1 ©
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§ STA 2023 c D.Wackerly  Lecture 17 233 3% at the level conﬁdence ). at the is true!! – NOTE: This DOES NOT mean that with ? conﬁdence ). level of level” ( or claim that the mean lifelength of all bulbs is larger than “ – In terms of this problem – – Conclusion : Is – RR : If we wanted signiﬁcance” ( or with at the , is AT THE “ Claim that the mean lifelength of all bulbs, £1
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¨ 1$ ! ¥ In terms of this problem: &% 2 ! LEVEL!! ¥ ! ) 235 and α − Zα If we are interested in : ? onesecond runs? Use 0 . “refute the claim” based on data for on average, at least 10 boards per second”. Evidence to printed circuit boards claims that “product can inspect, Ex. : #8.24, p. 333 Manufacturer inspection equip. for STA 2023 c D.Wackerly  Lecture 17 &% !
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¥ 10 6 7 8 level test level of signiﬁcance. In terms of this 9 10 8 RR : 7 11 10 9 10 11 6 9 12 12 9 10 8 9 10 enough evidence at the boards inspected per second is less than 10 .” level to indicate that the mean number of circuit application: “There at the 9 10 0 12 10 12 11 7 9 9 13 9 9 9 Must have actual data (not just and ). 1second runs. Data : 48 actual numbers Ex. # 8.24 Number of solder joints inspected in 48 Median
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§ § ¨ ¨ ¤ 11$ ¤ DISCUSSION SECTION Tuesday 11/5: EXAM 2 – During your Monday 11/4: OPTIONAL review 8.61, 8.67–69 Thursday : Exercises 8.29, 8.33, 8.34, 8.38–41, 8.59, Today: P. 334–338, 347–351 Assignments makes a pretty small package – (John Ruskin) Thought: When a man is wrapped up in himself, he 238 UNKNOWN population mean Last Time: Large Sample Hypothesis Testing about STA 2023 c D.Wackerly  Lecture 18 !
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¨$ § § § ¥ ¨ § £ Do you think that ? Recall the lightbulb example (P. 335) The pvalue or observed signiﬁcance level be rejected in favor of could ( IF we DO for which in favor of CONFIDENCE in our . What is the SMALLEST value of SO). decision to reject – Provides – Smaller
to reject is chosen BEFORE the test is performed Hypothesis Testing STA 2023 c D.Wackerly  Lecture 18 Agrees with twotailed test!! the 99% 242 conﬁdence interval — the value “ ” is ? . ¡ £ conﬁdence interval for Construct a © !
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§ 3% 243 3% &% the one observed pvalue = true. indicative that Probability of a zvalue Larger zvalues are pvalue ! ! ¦ rejection region STA 2023 c D.Wackerly  Lecture 18 ) ( ¨ ¨ ¨ is 244 – –
– REJECT . . . . .
. pvalue allows him/her to assess the “rareness” of the
observed event. 245 on a person
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£ 246 © ¥ STA 2023 c D.Wackerly  Lecture 18 § ¨2 247 ! (1) true proportion of Diet Coke drinkers who select Diet Pepsi in a blind taste test? indicate that a majority of the Diet Coke drinkers will the taste of Diet Pepsi. Is there sufﬁcient evidence to Coke and Diet Pepsi.
indicated that they preferred Coke drinkers were given unmarked cups of both Diet How??? (2) would select Diet Pepsi in a blind taste test. . the proportion of Diet Coke drinkers who Estimate for # of trials ; number of trials
in the sample size in the sample # of GOAL : Test hypotheses about trials based on a “large” the proportion of batteries that fail before select Diet Pepsi in a blind taste test. guarantee expires. 249 (Section 8.5) Recall the BINOMIAL EXPERIMENT. particular attribute ! ¡ UNKNOWN but FIXED PROPORTION of items with a ¡ ¡
Ex. : #8.68, p. 352 In a “Pepsi Challenge”, 100 Diet ¢ 2 Interested in a POPULATION that contains an ¢ &%
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3¡ ! Consider testing distribution. 3
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hypothesized value standard error is true Rejection Regions (RR): , OR OR has a STANDARD Hypothesized Value from NULL hypothesis Sheet Estimator and Standard Error from Formula estimator NORMAL distribution If &% STA 2023 c D.Wackerly  Lecture 18 £¦¥¡¥¡¥¡¥¡¥¡¥¡¥¡¥¡£¡¥¡¡ §
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indicated that they preferred true proportion of all voters who think health care reform is the leading priority Data : £ SAMPLE of all Diet Coke drinkers. Note: the the Pepsi Challenge are a (4) (3) 252 is “large” Assumptions : the 100 individuals participating in level test, RR : § ! ! © § ! ¡ ¥ § &%
£ ¡ ! select Diet Pepsi in a blind taste test? indicate that a majority of the Diet Coke drinkers will the taste of Diet Pepsi. Is there sufﬁcient evidence to Coke and Diet Pepsi. Coke drinkers were given unmarked cups of both Diet Ex. : #8.68, p. 352 In a “Pepsi Challenge”, 100 Diet STA 2023 c D.Wackerly  Lecture 18 ¨2 ¡ ( 34%
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reject AT THE level of signiﬁcance” ( or with Coke drinkers will select Diet Pepsi in a blind taste value?
value = test. 253 claim that there is sufﬁcient evidence at in favor of conﬁdence ) to indicate that the majority of Diet the “ In terms of this problem: LEVEL!! Conclusion : STA 2023 c D.Wackerly  Lecture 18 !
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2 ¨2 ¤ ! ¨ ! Basic Statistics 1 Proportion Sample
1 X
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100 Sample p
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90% CI
(0.462710, 0.657290) Test and Confidence Interval for One Proportion ZValue
1.20 PValue
0.115 Click Box “Use test and interval based on normal distribution”, OK, OK Click Options, Select Alternative, Type in Null Value 254 ! Number of trials, Number of Successes Click radio button “Summarized Data”, type in Stat Minitab? STA 2023 c D.Wackerly  Lecture 18 ¢ ! ! ¢ ...
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